So far so good for making the indirect estimates of group quarters population. However, I'm also trying to estimate standard errors based on Variance Replicate Tables for the two inputs (total population and population in households) and running into an issue. Since the two variables are dependent, I think we want:
SE(T – H) = SQRT(SE(T)**2 + SE(H)**2 – 2COV(T, H))
where T is total population and H is population in households.
However, this can result in negative values when SE(H) > SE(T), and I'm not sure how to handle those cases. These appear to be instances where the estimated group quarters population is greater than 0.